Something for the End of the Year?Author(s): David CrawfordSource: Mathematics in School, Vol. 29, No. 4 (Sep., 2000), pp. 21-22, 40Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30212360 .

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Something or the

end

end the year?

by David Crawford

'It's our last lesson of the year/term so do we have to do work today?' I am sure every teacher has heard pleas like this from pupils of all ages as a term draws to a close. I find trying to think of something the pupils will enjoy, as they do not think of it as work, and yet still be mathematically useful, quite difficult. Model making is always a possibility (leading to consideration of Euler's Theorem) and the polyhedral calendars published each year in MiS are very handy in that respect. However, with only short 35 minute lessons, as is the case in my school, this is not always a viable alternative given the time required to distribute equipment and to tidy up afterwards. In this short article I will present two other alternative suggestions (neither of which are in any way original) that I have used with some success in the past.

Mathematical Bingo The pupils are issued with a 4x4 grid as shown in Figure 1. They then have to place a number in each square so that it satisfies the condition given. Once all the group are ready, instead of drawing numbers out randomly, each pupil takes it in turn to call out a number until someone has completed their grid. The first time I play this with any group I usually find that the pupils have given their choice of number little thought beyond filling the description shown and so three

Mathematics in School, September 2000

or four circuits of the class are required before 'Bingo' is called. However, in later games, more strategy is applied as they search for numbers that can fit into more than one category, and so have more chance of being called by other members of the group. This gets them thinking about the structures of mathematics and, although a fun activity, serves as a useful development of their mathematical understanding.

Less Square than Even number Odd

40

Ends Multiple Factor Prime in of of

"2" 11 30

Over Power Under Between 25 of 5 50

10 and 60

Contains 3 digit Cube a number number Prime

"7"

Fig. 1 The game board for Mathematical Bingo

By careful choice of the categories used, this game could be used for pupils of different ages from primary all the way through to upper secondary and yet is so simple to set up and play.

Mathematical Abbreviations The second activity I use regularly is one often used by organizations as a fundraising quiz. It consists of a list of clues linking a number to a well known phrase for which only the initial letter of each key word is given along with the small, linking words such as 'and', 'in' or 'the'. For example, the phrase 7 Days in a Week would be abbreviated to 7 D in a W. As well as solving puzzles of this type, I find pupils enjoy thinking of examples of their own. However, these can get quite obscure and personal as I found on one occasion when the abbreviation 46 N of the H W M G L, which had stumped the whole class for a while, was finally revealed to be 46 Number of the House Where My Granny Lives! However, getting the pupils to think of all the occurrences of number in their everyday lives is, I think, a very useful and potentially enjoyable use of an end of term lesson.

These abbreviations can be general, as is the case for the ones shown in Figure 2 on page 22, or more mathematical, and hence more in keeping with my theme of developing mathematical thinking while having fun, as shown in Figure 3 on page 22. @

Keywords: Games; Properties of Number.

Author David Crawford, Leicester Grammar School, 8 Peacock Lane, Leicester LE1 5PX.

21

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Mathematical Abbreviations Find the missing words. Example: 11 P in F T Answer: 11 Players in a Football Team

1. 26 L of the A 2. 88 K on a P 3. 18 H on aG C 4. 24 HinaD 5. 57 HV 6. 15 FPinT 7. 147 H B in S 8. 1 FO the CN 9. 12 S of the Z

10. 6 MDM 11. 192 DE 12. 3 P C (R, B and Y) 13. 1815 BofW 14. 221b B S (H of S H) 15. 7 C of the R 16. 10 G B H on the W 17. 4 H of the A 18. 5 OR 19. 3 C (H H H) 20. 16 R in the B R (O and C) 21. 3 BM(SHTR) 22. 200 P F PG in M 23. 7 SaS 24. 1 W on a U 25. 1001 AN

Mathematical Abbreviations Find the missing words with a mathematical theme. Example: 21 E F N Answer: 21 Eighth Fibonacci Number

1. 90 D in aRA 2. 10 B of the D S 3. 49 SS 4. 180 ASof a T 5. 1024 B in a K 6. 75 T Q as aP 7. 50 L in RN 8. 144 aG or aDD 9. 20 F on an I

10. 120 FF 11. 111 S as a B N 12. 5 N of P S 13. 10000 S C in a S M 14. 2 OEP 15. 2 E A in an IT 16. 22 Y in aC 17. 135 I A of a R O 18. 6 FPN 19. 34 M C of an O F M S 20. 12 E on a C 21. 4 V on aT 22. 97 LPLTOH 23. 4 Ain a Q 24. 186280 S of L (M P S) 25. 42 A to L the U and E

Fig. 2 Mathematical Abbreviations - everyday version (answers on page 40)

Fig. 3 Mathematical Abbreviations - the mathematical version (answers on page 40)

PAENTALWITHS

XctW1A~uFtTBALLS by Terry Tuffnell

Over the last few years I have used the mental maths football game to improve the mental abilities of the children in my classes. This went down particularly well during the World

Cup as you can well imagine. The games can either be played as part of a league season, in which case you can get some of

your class to arrange a fixture list, and play games each week, or the games can be played as cup matches. Do be prepared for noisy lessons, particularly when the game is being played for the first few times. It is also advisable to devise some sort of refereeing to overcome disputed moves.

22

I also use yellow and red cards to deal with over- exuberance. The game works well with 2 players per side but there is no reason why it has to be this number. F

Keywords: Game; Mental Arithmetic.

Editor's Note: Terry has also devised mental maths games for Ten-pin bowling, Golf, Snooker and Tennis. If there is sufficient interest from readers, these could also be featured in future issues of MiS.

Author Terry Tuffnell, Mathematics Co-ordinator, Roysia Middle School, Royston, Hertfordshire SG8 5EQ.

Mathematics in School, September 2000

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Editor's Note: The author acknowledges the difficulty of the challenge and invokes, in his solutions, inverse trig functions, percentages and Fermat numbers. He invites readers to construe this as brilliant imagination or exceeding the bounds of the usual rules. The choice is yours.

The

The The CHALLENGE

by Patrick Trowbridge

As predicted by David Crawford (1999) it was a very daunting task to create numbers up to 100 using only the digits from 2000. Paul Chambers (2000) has published the first twelve. The rest can be formed if one is allowed to use inverse trigonometric functions (results in degrees), the % sign and the standard definition of a Fermat number, namely, that Fn = 22n + 1. (See page 41.)

References Chambers, P 2000 '2000', Mathematics in School, 29, 1. Crawford, D. 1999 '1999 The End of an Era', Mathematics in School, 28, 4.

Keywords: 2000; Puzzle.

Author Patrick Trowbridge, St Thomas More School, Blaydon, Tyne and Wear NE21 4BQ.

Something for the End of the Year? - Answers for pages 21 and 22

Answers: Everyday Version 1. 26 2. 88 3. 18 4. 24 5. 57 6. 15 7. 147 8. 1 9. 12

10. 6 11. 192 12. 3 13. 1815 14. 221b 15. 7 16. 10 17. 4 18. 5 19. 3 20. 16

21. 3 22. 200 23. 7 24. 1 25. 1001

Letters of the Alphabet. Piano Keys. Holes on a Golf Course. Hours in a Day. Heinz Varieties. First Point in Tennis. Highest Break in Snooker Flew Over the Cuckoo's Nest. Signs of the Zodiac. Million Dollar Man. Directory Inquiries. Primary Colours (Red, Blue and Yellow). Battle of Waterloo. Baker Street (Home of Sherlock Holmes). Colours of the Rainbow. Green Bottles Hanging on the Wall. Horsemen of the Apocalypse. Olympic Rings. Cheers (Hip Hip Hooray). Rowers in the Boat Race (Oxford and Cambridge). Blind Mice (See How They Run). Pounds For Passing Go in Monopoly. Swans a Swimming. Wheel on a Unicycle. Arabian Nights.

Answers: Mathematical Version 1. 90 2. 10 3. 49 4. 180 5. 1024 6. 75 7. 50 8. 144 9. 20

10. 120 11. 111 12. 5 13. 10000 14. 2 15. 2 16. 22 17. 135 18. 6 19. 34

20. 12 21. 4 22. 97 23. 4 24. 186280 25. 42

Degrees in a Right Angle. Base of the Decimal System. Seven Squared. Angle Sum of a Triangle. Bytes in a Kilobyte. Three Quarters as a Percentage. L in Roman Numerals. A Gross or a Dozen Dozen. Faces on an Icosahedron. Five Factorial. Seven as Binary Number. Number of Perfect Solids. Square Centimetres in a Square Metre. Only Even Prime. Equal Angles in an Isosceles Triangle. Yards in a Chain. Interior Angle of a Regular Octagon. First Perfect Number. Magic Constant of an Order Four Magic Square. Edges on a Cube. Vertices on a Tetrahedron. Last Prime Less Than One Hundred. Angles in a Quadrilateral. Speed of Light (Metres Per Second). Answer to Life the Universe and Everything.

40 Mathematics in School, September 2000

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